Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces
Differential Geometry
2022-10-13 v3
Abstract
We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the pseudo-hyperbolic space which are limits of positive curves. We also discuss a compact Plateau problem. The required compactness arguments rely on an analysis of the pseudo-holomorphic curves defined by the Gauss lifts of the maximal surfaces.
Cite
@article{arxiv.2006.12190,
title = {Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces},
author = {François Labourie and Jérémy Toulisse and Michael Wolf},
journal= {arXiv preprint arXiv:2006.12190},
year = {2022}
}
Comments
last version before publishing. Statement of Theorem 7.1 for finite Plateau problem is now only true for deformable curves. The other main theorems are unchanged